reserve X for set,
        n,m,k for Nat,
        K for Field,
        f for n-element real-valued FinSequence,
        M for Matrix of n,m,F_Real;

theorem Th18:
  for F be set
  holds
  F is Function of TOP-REAL n, REAL
    iff
  F is Function of REAL-NS n, REAL
  proof
    let F be set;
    the carrier of TOP-REAL n = the carrier of REAL-NS n by Th4;
    hence thesis;
  end;
